He's also very good at dealing with Doc's recovery and I found him cutting right through my pills with bairs and well spaced uairs.
Yeah, the up-airs are pretty stupid. They prohibit Doc from going in the air at all. Not even allowed to RECOVER through the air, smh.
I don't really have a solution for what to do about being above the Falcon just yet. I just try my best to stay grounded.
Those up-tilts and f-tilts are good answers to most of Falcon approaches. F-tilts because they break up Falcon's dashdances and can keep him from running away so freely. Sadly, the f-tilts are easily countered by Falcon's shorthop game.
Up-tilt as you probably realized already, counters most of Falcon's shorthop game and can often land Falcon in big trouble if he gets stuck above your up-tilts with no jumps left.
If it was truly the up-airs and throws giving you the trouble against Hax, I'd try finding a way to avoid getting grab and experimenting with different ways of Di-ing the throws if he happens to get the grabs. Although, I'm not sure exactly how Hax got the grabs to begin with. But I think the solution lies there. Figure out what he did to get grabs on you, and look for a way of countering that.
You got this OTG, now go back and show Hax how tough Doc really is